Abstract

Congruences for total number parts functions associated to ranks of partitions are recently studied in many papers. In particular, Chan, Osburn and the author proved congruences for NT‾(b,k,n) (resp. NT2‾(b,k,n)) which denotes the total number of parts in the overpartitions of n with D-rank (resp. M2-rank) congruent to b modulo k. In this paper, we replace these congruences by equalities.

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